Be very careful what you wish for because you may end up in a foster home situation. You need to talk to your family members and discuss your issues with them and see if there can be a family solution. Grandparents, aunts, uncles, cousins, etc. They may be able to help you get her the help she needs.
If you want to be on your own i.e. emancipated, the first thing you need to do is have a plan that includes how you will support yourself. If you simply want to get out of your mother's home and you would like to live with your father AND he agrees, then he can file a petition with the court and your wishes will be given great weight. Explore that option with your father first, and if that won't work, then repost for more info. Good luck!
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